# Wafer Handing Robotic Arm Vibration Trajectory Planning Based on Graylag Goose Optimization

## TL;DR

This paper introduces a new method for planning robot arm movements in semiconductor manufacturing to reduce vibrations and improve precision using a Graylag Goose Optimization algorithm.

## Contribution

A novel vibration-suppression trajectory planning method using the Graylag Goose Optimization algorithm for wafer-handling robots is proposed.

## Key findings

- The GGO algorithm effectively solves multi-objective optimization problems with grouped global search and local optimization.
- Planned trajectories show minimal displacement variation and low velocity and acceleration errors under disturbances.
- Pareto-optimal solutions are achieved for motion time and residual vibration energy trade-offs.

## Abstract

In contemporary semiconductor manufacturing, wafer-handling robots are essential for achieving high-speed and high-precision wafer transportation. However, the demand for rapid motion and lightweight design introduces flexible transmission components that are prone to residual vibrations, which degrade positioning accuracy and system stability. To address this challenge, this paper proposes a vibration-suppression trajectory planning method based on the Gray Goose Optimization (GGO) algorithm. The proposed algorithm integrates grouped global search with local optimization capabilities, making it well suited for solving multi-objective optimization problems. Comparative tests conducted on eight randomly selected multimodal benchmark functions from the CEC2013 test suite verify the effectiveness and robustness of the GGO algorithm. Establishing a multi-objective function that considers both motion time and vibration energy enables the GGO algorithm to determine the switching time points of an S-shaped velocity profile, thereby generating smooth trajectories with continuous velocity and acceleration. By varying different initial conditions, the trade-off between motion time and vibration energy is systematically analyzed with respect to angular displacement, initial acceleration, and time-weighting factors. Simulation results indicate that the planned trajectories exhibit negligible displacement variation under zero-mean disturbances. The velocity error remains within 0.1 deg·s−1, and the acceleration error is confined within 0.2 deg·s−2. Consequently, Pareto-optimal solutions are successfully obtained with respect to both motion time and residual vibration energy.